Question

1. A vending machine pours an average of 8.0 oz of coffee with a standard deviation of 0.2 oz if it is functioning properly. An inspector wants to take 16 cups of coffee from the machine to see if the machine is functioning well or not. He wants to have a significance level (alpha ) of 4%. (i) State the null and the alternative hypothesis . Is it a one-sided or two-sided test problem? (ii) Compute the power of test when the true average is equal to 7.8. (iii)Suppose the average of a sample of 16 cups turned out to be equal to 7.7 oz. Find the p-value ? (iv) Should the null hypothesis be rejected at alpha= 4% ?

Answer #1

A vending machine dispenses coffee. The average cup of coffee is
supposed to contain 7.0 ounces. Eight cups of coffee from this
machine show the average content to be 7.3 ounces with a standard
deviation of 0.5 ounce. Using a 5% level of significance, test
whether the machine has slipped out of adjustment and if the
average amount of coffee per cup is different from 7 ounces.
State the null and alternate hypotheses

A manufacturer of coffee vending machines has designed a new,
less expensive machine. The current machine is known to dispense an
average of 6 fl. oz., with a standard deviation of .2 fl. oz., into
cups. When the new machine is tested using 15 cups, the mean and
the standard deviation of the fills are found to be 6 fl. oz. and
.212 fl. oz. Test H0: σ = .2 versus Ha: σ ≠ .2 at levels of
significance .05...

A coffee machine is supposed to dispense 12 ounces of coffee in
each cup. A business using one of these machines is concerned that
it is dispensing less than 12 ounces. An inspector takes a sample
of 16 cups of coffee, and finds a mean of ¯x=11.7x¯=11.7 ounces
with a standard deviation of s=0.8s=0.8 ounces. (Assume coffee
serving volumes are normally distributed.)
1. What are the null and alternate hypotheses for this study?
H0: μ (< > ≤ ≥ =...

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